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Complexity and Evolution of Dissipative Systems focusses on the dynamic complexity of neural and genetic networks, reaction diffusion systems and equations of fluid dynamics. The author shows that all robust attractors can be realized in dynamics of such systems. In particular, a positive solution of the Ruelle-Takens hypothesis for Navier Stokes equations is given.
Complexity and Evolution of Dissipative Systems considers viability problems for such systems – viability under extreme random perturbations – and discusses an interesting hypothesis of M. Gromov and A. Carbone on biological evolution. There appears a connection with the Kolmogorov complexity theory. As applications, transcription-factors-microRNA networks are considered, patterning in biology, a new approach to estimate the computational power of neural and genetic networks, social and economical networks, and a connection with the hard combinatorial problems.